Slip in the Presence of Semi-Circular Menisci Between Parallel Ridges

Surfaces which are structured on the micro- and nanoscale to resist wetting are being considered for internal flows due to their drag reducing properties in applications such as electronics cooling and lab-on-chip. Here, an expression is developed to characterize the hydrodynamic slip in a laminar flow which occurs near the surface for the case when positive meniscus curvature is present. The surfaces considered are composed of ridges oriented parallel to the flow. Curvature of the meniscus, which resides between the liquid in the Cassie state and the gas trapped in cavities between the ridges, results from the pressure difference between the liquid and the gas. The meniscus is considered shear free. The no slip condition exists at the tips of the ridges. Conformal maps from the literature are used to derive an expression which is a function of cavity fraction of the surface. The positive protrusion angle is 90 degrees. Cavity fractions range from 0 to 75%.